A solid sphere of uniform density and radius $R$ cools radiatively with a time constant $\tau$ as per the following expression:
$T(t)=T_s+\left(T_h-T_s\right) e^{-t / \tau}$
where $T_h$ is the initial temperature of the object and $T_s$ is the surrounding temperature. Then,

• A

  $\tau \propto R^2$
• Correct answer
  B

  $\tau \propto R$
• C

  $\tau \propto R^3$
• D

  $\tau \propto R^0$

Hence, the correct answer is option: 'B'.